David M. Bressoud

Books

A
Radical Approach to Lebesgue's Theory of IntegrationThis
is a sequel to A Radical Approach to Real Analysis
(ARATRA). That book ended with Riemann's definition of the integral. That
is where this text begins. All of the topics that one might expect to
find in an undergraduate analysis book that were not in ARATRA are contained
here, including the topology of the real number line, fundamentals of
set theory, transfinite cardinals, the Bolzano–Weierstrass theorem,
and the Heine–Borel theorem. I did not include them in the first
volume because I felt I could not do them justice there and because, historically,
they are quite sophisticated insights that did not arise until the second
half of the 19th century.
This book owes a tremendous debt to Thomas Hawkins' Lebesgue's Theory
of Integration: Its Origins and Development. Like ARATRA, my book
is not intended to be read as a history of the development of analysis.
Rather, it is a textbook informed by history, attempting to communicate
the motivations, uncertainties, and difficulties surrounding the key concepts.
Click here for a list
of corrections.

A
Course in Computational Number Theory, co-authored with Stan Wagon,published
by Springer-Verlag under the Key
College Publishing label. We have a Mathematica file of the
strong pseduoprimes: StrongPseudoprimeData.m
and a list of corrections. The
file CNT.m is consistent with Mathematica
versions 6.0and 7.0.
This is an introduction to number theory couched in an exploratory, computation
rich setting that makes extensive use of Mathematica. Topics include
the Euclidean Algorithm, modular arithmetic, linear congruences, Chinese
Remainder Theorem, Fermat's Little Theroem and pseudoprimes, Euler's phi,
perfect numbers, primitive roots and orders, distribution of primes, prime
testing and certification, RSA, check digits, factoring algorithms, quadratic
residues and reciprocity, Pepin's test, continued fractions, Pell's equation,
CFRAC, Lucas sequences for prime certification and factorization and the
Lucas-Lehmer algorithm, representations as sums of squares, Gaussian primes.

Proofs
and Confirmations: the Story of the Alternating Sign Matrix Conjecture,
published jointly by the Mathematical Association
of America (Spectrum Series) and Cambridge
University Press (or Cambridge University
Press, NY) 1999. This is the story of the proof of the alternating
sign matrix conjecture written at a level accessible to anyone who has
had a course in linear algebra. It describes recent research in algebraic
combinatorics, using this example to illustrate the surprising twists
and turns of actual mathematical research. It is also an opportunity to
explore some of the related fields that fed into the ultimate solution.
These include partition theory, plane partitions, symmetric functions,
hypergeometric and basic hypergeometric series, lattice path counting
problems, and the Yang-Baxter equations of statistical mechanics. A notebook
of the Mathematica commands is available
as well as corrections. Solutions
and hints for selected exercises in chapters 1-4 are available as either
a PostScript or a PDF file. Note that for some reason I do not understand,
the latter is upside down which is not a hindrance if you want to print
it, but does make it difficult to read it from a screen. Kim-Ee Yeoh at Wisconsin has posted
JAVA programs for finding and counting alternating sign matrices.

A
Radical Approach to Real Analysis 2nd edition, Mathematical
Association of America, 2006. This is an introduction to real analysis
that begins with the problems the led to the development of this subject.
It starts with Fourier series and the difficulties it presented for mathematicians
of the early 1800s. It presents both successes and failures and explains
how and why the fundamental definitions and theorems of real analysis
came to be.

Click here
to access the Web Resources for the second edition
of A Radical Approach to Real Analysis

Factorization
and Primality Testing, Springer-Verlag,
1989. This is really an introduction to Number Theory that is built around
around the twin problems of how to determine whether a large integer is
prime and, if it is not, how to factor it into its prime factors. It includes
descriptions of the RSA public-key cryptosystem, the Multiple Polynomial
Quadratic Sieve, and the Elliptic Curve methods for factorization and
primality testing. Available ftp files include corrections
and a pdf file of the corrections.

Insights and Recommendations from the MAA National Study of College Calculus.
MAA Notes Volume, 2015. Edited by David Bressoud, Vilma Mesa, and Chris
Rasmussen. Results of a five-year study of mainstream post-secondary
Calculus I in the United States. Eleven articles by 17 of the
researchers who worked on the NSF project Characteristics of Successful Programs in College Calculus. PDF is available for free download.

The Rademacher Legacy to Mathematics, edited with George Andrews
and L. Alayne Parson, The Centenary Conference in Honor of Hans Radmacher,
July 21-25, 1992, The Pennsylvania State University, #166 in Contemporary
Mathematics.American Mathematical Society,
Providence, Rhode Island. 1994.

Analytic and Combinatorial Generalizations of the Rogers-Ramanujan
Identities, Memoirs of the American Mathematical Society #227, March,
1980